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In this paper, we consider the Anderson acceleration method for solving the contractive fixed point problem, which is nonsmooth in general. We define a class of smoothing functions for the original nonsmooth fixed point mapping, which can…

Optimization and Control · Mathematics 2024-12-11 Zekai Li , Wei Bian

Optimising a ranking-based metric, such as Average Precision (AP), is notoriously challenging due to the fact that it is non-differentiable, and hence cannot be optimised directly using gradient-descent methods. To this end, we introduce an…

Computer Vision and Pattern Recognition · Computer Science 2020-09-10 Andrew Brown , Weidi Xie , Vicky Kalogeiton , Andrew Zisserman

In this paper we discuss approximation of partially smooth functions. The problem arises naturally in the study of laminated currents.

Dynamical Systems · Mathematics 2015-06-26 John Fornaess , Yinxia Wang , Erlend Fornaess Wold

In this paper, we analyze the performance of randomized benchmarking protocols on gate sets under a variety of realistic error models that include systematic rotations, amplitude damping, leakage to higher levels, and 1/f noise. We find…

Quantum Physics · Physics 2014-07-08 Jeffrey M. Epstein , Andrew W. Cross , Easwar Magesan , Jay M. Gambetta

In this paper, we consider the problem of minimizing the average of a large number of nonsmooth and convex functions. Such problems often arise in typical machine learning problems as empirical risk minimization, but are computationally…

Machine Learning · Statistics 2018-05-21 Wenjie Huang

The main issues of the original Symmetrical smoothing method consists of approximation of the extremal volume of the set by the smooth symmetric function (sum of step functions) and then solve the optimization problem. when making…

Combinatorics · Mathematics 2017-03-10 Vladimir Blinovsky

One strategy for adversarially training a robust model is to maximize its certified radius -- the neighborhood around a given training sample for which the model's prediction remains unchanged. The scheme typically involves analyzing a…

Machine Learning · Computer Science 2021-04-14 Xingjian Zhen , Rudrasis Chakraborty , Vikas Singh

We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…

Logic in Computer Science · Computer Science 2017-12-12 Aleksandar Zeljic , Peter Backeman , Christoph M. Wintersteiger , Philipp Ruemmer

Estimating the sound absorption in situ relies on accurately describing the measured sound field. Evidence suggests that modeling the reflection of impinging spherical waves is important, especially for compact measurement systems. This…

Audio and Speech Processing · Electrical Eng. & Systems 2024-04-18 Eric Brandao , William Fonseca , Paulo Mareze , Carlos Resende , Gabriel Azzuz , Joao Pontalti , Efren Fernandez-Grande

As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…

Quantum Physics · Physics 2024-07-26 Nicola Franco , Marie Kempkes , Jakob Spiegelberg , Jeanette Miriam Lorenz

An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…

Optimization and Control · Mathematics 2026-04-02 Albert S. Berahas , Frank E. Curtis , Lara Zebiane

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available…

Methodology · Statistics 2025-10-30 Dominik Sturm , Ivo F. Sbalzarini

Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…

Numerical Analysis · Mathematics 2024-07-19 Camille Pouchol , Marc Hoffmann

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…

Discrete Mathematics · Computer Science 2025-10-20 Chengpu Wang

We revisit the error correction scheme of real-valued signals when the codeword is corrupted by gross errors on a fraction of entries and a small noise on all the entries. Combining the recent developments of approximate message passing and…

Information Theory · Computer Science 2014-02-04 Jean Barbier , Florent Krzakala , Lenka Zdeborová , Pan Zhang

Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cancellation rather than error accumulation, resulting in slower…

Numerical Analysis · Mathematics 2024-10-15 Petros Drineas , Ilse C. F. Ipsen

Real-world measurement noise in applications like robotics is often correlated in time, but we typically assume i.i.d. Gaussian noise for filtering. We propose general Gaussian Processes as a non-parametric model for correlated measurement…

Machine Learning · Statistics 2019-09-25 Vince Kurtz , Hai Lin

Data noising is an effective technique for regularizing neural network models. While noising is widely adopted in application domains such as vision and speech, commonly used noising primitives have not been developed for discrete…

Machine Learning · Computer Science 2017-03-09 Ziang Xie , Sida I. Wang , Jiwei Li , Daniel Lévy , Aiming Nie , Dan Jurafsky , Andrew Y. Ng

We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…

Statistics Theory · Mathematics 2020-11-10 Yair Ashlagi , Lee-Ad Gottlieb , Aryeh Kontorovich

With the growing integration of AI in daily life, ensuring the robustness of systems to inference-time attacks is crucial. Among the approaches for certifying robustness to such adversarial examples, randomized smoothing has emerged as…

Computation and Language · Computer Science 2024-08-02 Zhuoqun Huang , Neil G Marchant , Olga Ohrimenko , Benjamin I. P. Rubinstein